Unique Parameters Selection Strategy of Linear Canonical Wigner Distribution via Multiobjective Optimization Modeling

There are many kinds of linear canonical transform (LCT)-based Wigner distributions (WDs), which are very effective in detecting noisy linear frequency-modulated (LFM) signals. Among WDs in LCT domains, the instantaneous cross-correlation function type of Wigner distribution (ICFWD) attracts much attention from scholars, because it achieves not only low computational complexity but also good detection performance. However, the existing LCT free parameters selection strategy, namely a solution of the expectation-based output signal-to-noise ratio (SNR) optimization model, is not unique. In this paper, by introducing the variance-based output SNR optimization model, a multiobjective optimization model is established. Then the existence and uniqueness of the optimal parameters of ICFWD are investigated. The solution of the multiobjective optimization model with respect to one-component LFM signal added with zero-mean stationary circular Gaussian noise is derived. A comparison of the unique parameters selection strategy and the previous one is carried out. The theoretical results are also verified by numerical simulations.